Formability Characterization of Sheet Metals using the Angular Stretch Bend Test
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Date
2023-06-15
Authors
Aydemir, Nicholas
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Publisher
University of Waterloo
Abstract
This thesis investigates the mechanics of the angular stretch bend test (ASBT) and analytical models using three different advanced high strength steels (AHSS) and finite element simulation. The three steels, 590R, 3rd Gen 1180, and DP980 were characterized using the ASBT. The accuracy of models from the literature used to eliminate process dependent effects such as bending, and tool contact pressure were evaluated with the experimental data. A finite element model was developed to further investigate the process correction models.
Historically, the automotive forming industry has relied upon in-plane experimental methods to produce forming limit curves (FLCs) but this can lead to overly-conservative component designs as they ignore the beneficial effects of bending and tool contact pressure that delay the onset of tensile instability, both of which are present in the ASBT. The ASBT in plane strain tension can be characterized by the bend severity which is the ratio of the blank thickness to the punch radius. The bend severity is a useful parameter but does not consider the strain path or other test parameters such as the die gap width or entry radii. To assess the effect of the die gap, a new ASBT die set was designed and used in the experimental work in this thesis. The focus of the experimental work was on three grades of automotive advanced high strength steels: 590R, DP980, and 3rd Gen 1180. Full-field strain measurements were obtained using stereo-digital image correlation (DIC). The experimental results showed that the strain paths were controlled by the bend severity and sample width while the die gap width played a secondary role.
Analytical models have been proposed in the literature to reconcile the differences between limit strains obtained using different experimental test methods. The models involve measuring surface curvature, calculating thickness based upon the curvature and surface strains, accounting for non-linear strain paths (NLSP) for linearization of the limit strains and compensating for tool contact pressure. The curvature model was found to be sensitive to the size of the measurement window with a 20 mm window recommended. The thickness model studied from the literature was relatively complex, so a new analytical model was developed for the ASBT to determine the thickness across the range of practical bend severities from 0.14 to 1.4 using the curvature and surface strains. The new proposed ASBT thickness model was in good agreement with the finite-element data with comparable accuracy to the more complex models in the literature.
The influence of non-linear strain paths (NLSP) was found to be relatively minor in the ASBT as the strain paths were relatively linear and near plane strain. The achievable strain paths in the current ASBT using a cylindrical punch were constrained to intermediate uniaxial tension to plane strain tension. Overall, the minimal influence of NLSP on the ASBT is an advantage as the NLSP correction can be very sensitive to the limit strain detection algorithm as reported in the literature.
The analytical model to compensate for contact pressure in the literature was evaluated to the ASBT experiment data and produced promising results when comparing the pressure compensated limit strains to corresponding in-plane limit strain data. However, detailed finite element simulations of the ASBT showed that the contact pressure predicted by the model was significantly lower than the simulation values. The analytical model to compensate for the contact pressure appeared to work in some cases but is attributed to its systemic underprediction of the actual contact pressure tied with an extremely sensitive pressure correction tied to the hardening rate. It is believed that the high sensitivity to the hardening coupled with the underestimation of the contact pressure magnitude counterbalanced one another and led to reasonable corrections for the out-of-plane limit strains. Future work is required to improve the accuracy of the contact pressure model and to then re-visit the phenomenological mapping criterion used for the limit strains.
A finite element model was developed in conjunction with the experimental work to provide further insight to the models. A convergence study was performed on a plane-strain constrained ASBT model to determine the minimum number of through-thickness solid elements to obtain convergence in the strain field. Several methods to obtain contact pressure data from the finite-element simulations were considered as the contact area depends upon the solver and contact algorithms. It was observed that elastic tooling has a significant influence upon the contact pressure although the tooling is commonly idealized as rigid in metal forming simulations. Shell elements were also evaluated as they are the preferred element type in the forming industry but were not able to resolve the relatively high bend severities considered in this thesis.
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Keywords
formability, sheet metal, characterization, stretch bend, bending